Modeling of Multiple Scattering Effects in Fraunhofer Diffraction Particle Size Analysis

A model for the direct problem of calculating the forward scattering signature of a multiple scattering medium is presented. The new formulation is optimized for integration into schemes for reconstructing the particle size distribution from laser diffraction (forward scattering) signatures obtained from optically thick media. The analysis is valid for media where the particle sizes and interparticle spacings are large (relative to the wavelength and the particle size, respectively) such that Fraunhofer diffraction theory adequately describes the properties of the forward scattered light from individual scattering events. The simulated performance of laser diffraction particle sizing instruments was then studied using predictions of the scattered light signatures which would be measured by laser diffraction instrument under multiple scattering conditions. The results were compared with experimental data and theoretical calculations based on other models.     

Customizable web service interface for light scattering simulation programs

Investigation of light scattering by simulations became increasingly important in recent years. Applications range from plasmonics to optical particle characterization. While there are hundreds of programs available, using them can be very time consuming: installation, configuration and operation often are laborious. As a result potential users of such software might be discouraged by the complexity of the necessary tasks. Not only ‘casual users’ – scientists who need light scattering simulation results for their daily work but who are not specialized on the topic – could benefit from tools to execute the calculations online via an easy to use web-interface accessed by a browser. In this case no local installation of the software is necessary, a user friendly interface helps learning and understanding the use of programs, while calculations can be done from anywhere and any time as long as a user is connected to the internet.This paper describes a newly developed interface that can be used for these purposes. It is made freely available to everyone and can be adapted to a variety of existing light scattering programs.     

Relevance of Reflection in Static and Dynamic Light Scattering Experiments

Using a monodisperse PMMA dispersion, it was shown that light reflection at the sample cuvette walls may greatly influence the results of both static (SLS) and dynamic (DLS) light scattering experiments. Considering SLS, this reflection phenomenon mostly causes an overestimation of the scattered intensity at high scattering angles, which may give rise to the emergence of an additional, artificial peak in the lower region of the particle size distribution. On the other hand, the influcence of reflection on DLS measurements was shown to be particularly important in the upper region of the particle size distribution. The experimentally observed phenomena were explained from the basic principles of both particle sizing methods. Finally, it was shown that the disturbing effect of reflection could be avoided by modifying either the hardware or the software of the static and dynamic light scattering technique.     

Scattering and Transmission by a Monolayer of Spheres: A Study on the Monolayer Structure

The angular distribution of scattered light and the transmission of radiation through a monolayer of monodisperse spherical particles at variable particle concentration are studied. The scattering of light by a single particle is calculated with the classical Lorentz‐Mie theory. For a monolayer of mono‐dispersed spherical particles, if the monolayer density is less than 0.5 and the particle size parameter is larger than 5, effects from multiple scattering and dependent scattering can be excluded so that only steric interactions are considered. It is found that the scattering pattern, especially in the forward and backward directions, and the transmission are strongly dependent on the monolayer density.     

Reflection Phenomena in Particle Sizing by static and dynamic light scattering

Using a monodisperse poly(methyl methacrylate) dispersion it was shown that light reflection at the sample cuvette walls may greatly influence the results of both static (SLS) and dynamic (DLS) light scattering experiments. Considering SLS, this reflection phenomenon mostly causes an overestimation of the scattered intensity at high scattering angles, which may give rise to the emergence of an additional, artificial peak in the lower region of the particle size distribution. On the other hand, the influence of reflection on DLS experiments was shown to be particularly important in the upper region of the particle size distribution. The experimentally observed phenomena were explained from basic principles of both particle sizing methods. Finally, it was shown that the disturbing effect of reflection could be avoided by modifying either the hardware or the software of the SLS and DLS techniques.     

Light scattering theories and computer codes

In aerosol science today light scattering simulations are regarded as an indispensable tool to develop new particle characterization techniques or in solving inverse light scattering problems. Light scattering theories and related computational methods have evolved rapidly during the past decade such that scattering computations for wavelength sized nonspherical scatterers can be easily performed. This significant progress has resulted from rapid advances in computational algorithms developed in this field and from improved computer hardware.In this paper a review of the recent progress of light scattering theories and available computational programs is presented. We will focus on exact theories and will not cover approximate methods such as geometrical optics. Short outlines of the various theories are given alongside with informations on their capabilities and restrictions.     

Determination of the Refractive Index of Water‐dispersible Granules for Use in Laser Diffraction Experiments

Modern laser light scattering equipment can cover a very broad particle size range by using complex algorithms, such as the Mie theory. A disadvantage of this theory, however, is that it requires the knowledge of the refractive index of the particles, which is not straightforward for powdered organic substances. In this study, thiram, a common dithiocarbamate fungicide, was used as a model compound. In a first part, a method was elaborated to determine the refractive index, based on refractive index measurements of solutions of the compound of interest in a range of solvents. Two different extrapolation techniques were compared. Both techniques were validated by applying them to the determination of the refractive indices of poly(vinyl acetate) and poly(methyl methacrylate). Secondly, the influence of the refractive index value on the generated particle size distribution in the laser diffraction software was investigated. It was observed that widely different particle size distributions can be generated by the laser diffraction software for a single experimental data‐set. Therefore, accurate refractive index information is required to obtain reliable particle size distribution results.     

Fractal Character of Dynamic Light Scattering of Particles

Dynamic light scattering signals from particles, exhibit fractal characteristics. This feature can be used to determine the particle size. The use of the fractal dimension, as a quantitative method to analyze the properties of dynamic light scattering signals from submicron particles, is presented. The analysis is performed directly on the time‐resolved scattered intensity, and the Box Dimensions of light scattering signals of particles with diameters 100, 200, 500 and 1000 nm. The experimental results show that the fractal dimensions of light scattering signals correlate well with particle size. In the submicron size range, the smaller the particles, the larger their fractal dimensions. Compared with the PCS technique, only several hundreds of samples are required in the fractal method. Therefore, the data processing is easily accomplished. However, this method only provides the mean particle size, but not the particle size distribution.     

Generalized Lorenz‐Mie Theory for a Sphere with an Eccentrically Located Inclusion,and Optical Chaos

This paper deals with the case when a homogeneous spherical particle (called the inclusion) is embedded at an arbitrary location inside a sphere (called the main or host sphere). Similarly as for previous Generalized Lorenz‐Mie Theories, many applications are expected from this theory, in particular in the field of optical particle characterization. Another interesting prospect concerns the behavior of morphology‐dependent resonances (MDRs). From an electromagnetic point of view, these MDRs correspond to solutions of characteristic equations associated with boundary conditions and lead to internal fields which are concentrated near the rim of the scatterer. It is also shown that this geometrical optics approximation (expressed in terms of rays) is equivalent to a mechanical problem (expressed in terms of trajectories). This mechanical problem leads to chaotic behavior corresponding to optical chaos phenomena in the optical language. We therefore exhibit a class of particles (i) for which the electromagnetic problem is exactly solvable in the framework of a GLMT and (ii) which exhibits chaotic signatures. It is expected that these chaotic signatures would be revealed in salient features of the scattering diagrams, opening the way to refined optical particle characterization in the presence of inhomogeneities.     

A Theoretical and Experimental Study to Measure the Concentration and Particle Size Distribution in Two‐Phase Flows

Based on light scattering theory, an optical method is presented for measuring the concentration and particle size distribution of the dispersed phase in two‐phase flows. A prototype was also constructed. Comprehensive computer simulation and numerical calculations were carried out to calibrate the correctness of this method. An experimental study was also performed in gas–solid and gas–liquid two‐phase flows. The results of the measurements are given and discussed in detail.     

Hardware and software for ground tests of onboard charged particle spectrometers

The article presents a hardware and software complex for ground tests of onboard charged particle spectrometers that are designed at the National Research Nuclear University MEPhI for monitoring of nuclear-physical factors of space weather and can be installed in a wide class of satellites. The structural scheme and operating principles of component parts are discussed. The main algorithm and software features are presented. The technique of ground spectrometer tests and calibrations in various measurement modes at atmospheric cosmic particle flows, both in autonomous laboratories and in interface tests as part of a satellite, is also described.     

Matter-wave scattering on a BEC in a double-well potential

We study the inelastic scattering of a probe particle on a Bose-Einstein condensate confined in a double-well potential. We identify prominent signatures of the underlying mean-field phase space in the scattering signal and derive an analytical expression for the inelastic scattering cross section.     

Depolarization by aerosols: Entropy of the Amsterdam light scattering database

In this paper we apply an entropy analysis to measured scattering matrices from the Amsterdam light scattering database. We select examples of mineral aerosols from the database and use them to demonstrate differences in polarization behavior between the particle clouds using a new coherency matrix formulation. These differences are further investigated by analyzing the polarized component of the matrices via two new eigenvector parameters, which can be mapped conveniently onto the surface of a sphere, analogous to the Poincaré sphere used for wave states. We conclude by considering the potential for discriminating different aerosols on the basis of their entropy/eigenvector signatures by solving the contrast optimization problem for clouds with different scattering matrices by using a novel generalized coherency eigenvalue formulation.     

孤立波在一维复合颗粒链中传播特性的模拟研究

采用分子动力学方法模拟研究了孤立波在重轻颗粒相间排列的一维复合颗粒链中的传播特性.结果发现,在轻重颗粒的质量比较大或较小时,散射作用较弱,颗粒的速度和孤立波的速度衰减较慢.在轻重颗粒的质量比为中等时,散射作用较强,颗粒的速度和孤立波的速度衰减较快.孤立波在通过重-轻颗粒界面时,存在有增速效应,可以提高孤立波的传播速度.并且,轻重颗粒的质量比越小增速效应越强.在散射作用和增速效应的共同作用下,改变轻重颗粒的质量比可以调控孤立波在重-轻颗粒链中的传播时间.     

Synchrotron radiation refraction topography for characterization of lightweight materials

The employment of synchrotron radiation for refraction topography of materials has considerable advantages over standard x‐ray sources. The much higher beam intensity and the parallel and monochromatic radiation provide faster measurements and better angular and spatial resolution. X‐ray refraction techniques image the inner surface and interface concentration of micro‐structured materials. This effect of x‐ray optics is additional to small‐angle scattering by diffraction, when the scattering objects reach micrometre dimensions. We have developed x‐ray refraction techniques within the last decade in order to meet the growing demands for improved non‐destructive characterization of high‐performance composites, ceramics and other low‐density materials. Sub‐micron particle dimensions, the pore size of ceramics, the crack density distribution and single fibre debonding within damaged composites can be measured and visualized by computer‐generated interface topographs. For this purpose investigations are now being performed at the new hard x‐ray beamline of the Federal Institute for Materials Research and Testing (BAM) at BESSY, Berlin. This BAMline provides monochromatic radiation of photon energies from 5 to 60 keV from a double multilayer and/or a double‐crystal monochromator. A separate instrument is dedicated to the further development and application of synchrotron radiation refraction (SRR) topography. Different from conventional small‐angle scattering cameras with collimating slits and pinholes, scattering angles down to a few seconds of arc are selected by a single‐crystal analyser, similar to a Bonse–Hart diffractometer. A 20 µm spatial resolution of the scattering micro‐structures is achieved by a CCD camera with a fluorescent converter. First SRR topographs of aircraft composites [carbon fibre‐reinforced plastics (CFRP), carbon fibre‐reinforced ceramics (C/C), metal matrix ceramics (MMC)] will be reported. Copyright © 2004 John Wiley & Sons, Ltd.     

RixsToolBox: software for the analysis of soft X‐ray RIXS data acquired with 2D detectors

A software with a graphical user interface has been developed with the aim of facilitating the data analysis for users of a new resonant inelastic X‐ray scattering (RIXS) spectrometer installed at the ESRF beamline ID32. The software is organized in modules covering all relevant steps in the data reduction from a stack of several hundred two‐dimensional CCD images to a single RIXS spectrum. It utilizes both full charge integration and single‐photon centroiding to cope with high‐flux and high‐resolution requirements. Additional modules for further data analysis and the extraction of instrumental parameters are available. The software has been in routine use for about a year now and in that time many additional features have been incorporated. It now meets the users' need for an easy‐to‐use data analysis tool that allows looking at and understanding data as it is acquired and thus steering users' experiments more efficiently.     

Superposition rule for light scattering by a composite particle

A superposition rule for light scattering by composite particles is presented that expresses the scattering amplitude of a composite particle as a superposition of that of the host particle and those of the shadowed inclusions. The superposition rule is derived for a soft composite particle but also provides insight into light scattering by a general composite scatterer. Favorable comparison with an exact numerical method demonstrates the usefulness of the rule in analyzing light scattering by composite particles such as biological cells.     

Particle Systems Characterization Using a Flat Cell Static Light Scattering Apparatus

In this work a light scattering apparatus for the study of heterogeneous liquid systems of evolving morphology is presented. A Fraunhofer configuration consisting of a linear array of photodiodes is used to detect the light scattered by thin samples illuminated by a He‐Ne laser light. Temperature control is available. The instrument is tested with the polymerization induced phase separation of a thermosetting polymer formulated with a divinylester resin copolymerized with styrene and modified with poly(methylmethacrylate). The system is successfully modeled as an arrangement of particles growing in size and number, and varying in composition. The ability of the experimental setup to provide results that can be quantitatively analyzed is checked using microspherical polystyrene standards. Different samples with nominal sizes of 0.5, 1 and 2 μm are used in different combinations of sample thickness and concentration. The analysis of the light scattering spectra is performed using inverse techniques to estimate the particle size distribution of the microspheres. The results agree with previous knowledge of the parameters of the samples.     

Intercomparison of Inversion Algorithms for Particle‐Sizing Using Mie Scattering

The applicability of different inversion algorithms to retrieve a size distribution of particles in air from light scattering is examined. The investigation is focused on an optical measurement setup with an elliptical mirror as the main optical element. In order to evaluate the capabilities of the individual inversion methods, light scattering by spherical particles is simulated in the size ranges of 0.1 – 10 μm and 0.05 – 1 μm. The distribution of the particle diameters is modeled with three different parametric functions, i.e., RRSB, logarithmic‐normal and a more specific distribution from an ultrasonic nebulizer. Different kinds of noise, e.g., additive and/or multiplicative, are applied in different levels to the simulated scattering measurement to include real physical measurement conditions. The convergence properties of the scattering simulation are investigated with respect to the number of size classes, and thus, information concerning the size resolution required to simulate a measurement for a given particle size distribution is obtained. Further parameters of interest are the minimum angular resolution of the measurements, the number of size classes of the retrieved particle size distribution and the measured polarization of the scattered light.     

Particle Size Distributions from Static Light Scattering with Regularized Non‐Negative Least Squares Constraints

Simulated data from static light scattering produced by several particle size distributions (PSD) of spherical particles in dilute solution is analyzed with a regularized non‐negative least squares method (r‐NNLS). Strong fluctuations in broad PSD's obtained from direct application of NNLS are supressed through an averaging procedure, as introduced long ago in the inversion problem in dynamic light scattering. A positive correlation between the best PSD obtained from several averaging schemes and the condition number of the respective data transfer matrices was obtained. The performance of the method is found to be similar to that of constrained regularization (CONTIN), which uses also NNLS as a starting solution, but incorporates another regularizing strategy.